A303659 Numbers k such that the average of greatest prime factors of all positive integers <= k is an integer.

2, 5, 6, 24, 27, 28, 79, 1171, 1901, 1932, 7845, 19152, 360698, 649358, 1731441, 1979944, 30658517, 34337898, 400114748, 412626117, 3738454462, 7725156081, 97366414806, 129951504625, 290788509485

Offset

1,1

Comments

Numbers k such that (k - 1) | (A046670(k) - 1).

Numbers k such that (k - 1) | A088822(k).

a(26) > 10^12. - Giovanni Resta, May 05 2018

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Greatest Prime Factor

Example

6 is in the sequence because (gpf(2) + gpf(3) + gpf(4) + gpf(5) + gpf(6))/5 = (2 + 3 + 2 + 5 + 3)/5 = 3 is an integer.

Prog

(PARI) isok(n) = (n>1) && !(sum(k=2, n, vecmax(factor(k)[, 1])) % (n-1)); \\ Michel Marcus, Apr 29 2018
(PARI) lista(nn) = {s = 0; for (n=2, nn, s += vecmax(factor(n)[, 1]); if (! (s % (n-1)), print1(n, ", ")); ); } \\ Michel Marcus, Apr 29 2018

Crossrefs

Cf. A006530, A046670, A088822, A226647, A284755, A303480, A303482.

Sequence in context: A136324 A128367 A178924 * A250546 A137067 A214200

Adjacent sequences: A303656 A303657 A303658 * A303660 A303661 A303662

Keyword

nonn,more

Author

Ilya Gutkovskiy, Apr 28 2018

Extensions

a(13)-a(18) from Michel Marcus, Apr 29 2018

a(19)-a(25) from Giovanni Resta, May 05 2018

Status

approved